1. Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 MATLAB Programming Chapter 2

2. Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 2 MATLAB a flagship software which was originally developed as a matrix library. A variety of numerical functions, symbolic computations, and visualization tools have been added to the matrix manipulations. Demo programs: http://web.mst.edu/~ercal/228/MATLAB/1-2/analpara.m http://web.mst.edu/~ercal/228/MATLAB/1-2/analpara2.m http://web.mst.edu/~ercal/228/MATLAB/1-2/analpara4.mhttp://web.mst.edu/~ercal/228/MATLAB/1-2/analpara4.m % file I/O http://web.mst.edu/~ercal/228/MATLAB/1-2/numpara.m http://web.mst.edu/~ercal/228/MATLAB/1-2/numpara2.m

3. Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3 Sample Program g=9.8; cd=12.5; m = 68.1; dt = input('time increment (s):'); tf = input('final time (s):'); ti=0; vi=0; while (1) dvdt = g-(cd/m)*vi; vi = vi + dvdt*dt; ti = ti + dt; if ti >= tf, break, end end disp('velocity (m/s):') disp(vi) t (sec.)V (m/s) 00 219.60 432.00 844.82 1047.97 1249.96 ∞53.39 m=68.1 kg; c=12.5 kg/s; g=9.8 m/s

4. Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 4 Built-in functions sqrt(x) exp(x) abs(x) log(x) log10(x) factorial(x) TRIGONEMETRIC sin(x) sind(x) cos(x) cosd(x) tan(x) tand(x) cot(x) cotd(x) Rounding functions round(x) fix(x) - round towards zero ceil(x) floor(x) rem(x,y) – returns the remainder after x is divided by y (similar to % function in C) Display formats format short : 41.4286 format long: 41.42857142857143 format short e: 4.1429e+001 format long e: 4.142857142857143e+0001 format short g: 41.429 format long g: 41.4285714285714 format bank: 41.43 format compact: eliminates empty lines format loose: adds empty lines

5. Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 5 Plot function >> x=0:1:5 x = 0 1 2 3 4 5 >> y = sin(10*x) + cos(3*x) y = 1.0000 -1.5340 1.8731 -1.8992 1.5890 -1.0221 >> plot(x,y) >> xlabel('x in radians') >> ylabel('y = sin(10*x) + cos(3*x)') >> >> z = zeros(1,6) % alternative way z=0*x z = 0 0 0 0 0 0 >> plot(x,y, x,z) >> xlabel('x in radians') >> ylabel('y = sin(10*x) + cos(3*x)')

6. Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 6 Roots of polynomials >> r = [1, -2, 4] r = 1 -2 4 >> poly(r) ans = 1 -3 -6 8 >> p = poly(r) p = 1 -3 -6 8 >> solve = roots(p) solve = 4.0000 -2.0000 1.0000 System of equations >> x=[-1, 5] x = -1 5 >> A = [2, 3; -1, 4] A = 2 3 -1 4 >> b = A*x' b = 13 21 >> solveX = inv(A)*b solveX = 5.0000

7. Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 7 Passing a function as an argument The following program plots a function (passed as an argument) between a specified range (xa, xb): http://web.mst.edu/~ercal/228/MATLAB/1-2/myplot.m function draw = myplot(func, xa, xb, inc, LabelX, LabelY) X = xa:inc:xb Y = func(X); Z = 0*X; plot(X,Y,X,Z); xlabel(LabelX); ylabel(LabelY); function f1 = myfunc(x) % stored in another file called myfunc.m f1 = sind(x); MATLAB call: >> myplot(@myfunc, xmin, xmax, increment, LabelX, LabelY)

8. Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Fundamental control structures in MATLAB Managing Variables clear – removes all variables from memory clear x y – removes only x and y from memory who – displays a list of variables in the memory whos – displays a list of variables in the memory along with their size and class FOR-Loop sum = 0; DOFOR i = start, step, final for i = 2:1:25 (Loop Body) sum = sum + A[i]; ENDDO end

9. Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Spreadsheet that allows the user to enter and perform calculations on rows and columns of data. When any value on the sheet is changed, entire calculation is updated, therefore, spreadsheets are ideal for “what if?” sorts of analysis. Excel has some built in numerical capabilities including equation solving, curve fitting and optimization. It has several visualization tools, such as graphs and three dimensional plots. It also includes Visual Basic (VBA) as a macro language that can be used to implement numerical calculations. check out: http://www.anthony-vba.kefra.com/vba/vbabasic1.htmhttp://www.anthony-vba.kefra.com/vba/vbabasic1.htm EXCEL

10. Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.